{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yrZMpFF2Inp/35PAp/QBdRbZateyURHv3uo5EKZVTW7eGSQIOjAK6pj0oIpWB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\nXJIkSZKkEbgAlyRJkiRpBP8A7k6fk5EsncIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x921a0b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = np.arange(-4 * np.pi, 4 * np.pi, 0.001)\n",
    "convex = a**2\n",
    "concave = -a**2\n",
    "nonconvex = a**2 + 20 * np.sin(2*a)\n",
    "plt.figure(figsize=(17,5))\n",
    "plt.subplot(131)\n",
    "plt.plot(a, convex, color='r')\n",
    "plt.title('Convex', size=20)\n",
    "plt.grid(True)\n",
    "plt.subplot(132)\n",
    "plt.plot(a, concave, color = 'g')\n",
    "plt.title('Concave', size=20)\n",
    "plt.grid(True)\n",
    "plt.subplot(133)\n",
    "plt.plot(a, nonconvex, color = 'b')\n",
    "plt.title('Non-Convex', size=20)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HcBLAnxFRjb4RET1BRANENDAzM5OmpjH5RE//GF65Po2nvjMEX6MbK+ubOHG40fg8G42q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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa918cf0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = np.random.rand(1000)*10 - 5\n",
    "y1 = np.exp(-a**2) + np.random.randn(1000) * 0.07\n",
    "plt.scatter(a, y1, s=4, alpha=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ -1.15702698  -8.02070806  -3.13414265 -11.5330226   45.53441367\n",
      "  50.43115394  10.51993709  11.65412903  16.1566758    3.18062926\n",
      "  10.8979166    8.2385378    6.32883713  29.25199278  20.20411501\n",
      "  -8.97306874  10.1975223   11.9581736   -2.55007803  29.69027899\n",
      "  34.64414213  81.36063148  -1.49166392 -53.3202254   23.19252109\n",
      " -25.08749028   1.51320718   9.63165243  20.47984815 -12.55458836\n",
      "  20.63602179  97.17602509  51.09088916  30.11285562  16.34335423\n",
      "   8.07542912  36.89076606   3.40292018  15.76547735  39.01713136\n",
      "  19.39732725 -19.58834826   8.19093895   2.47194294  70.00118674\n",
      "   9.29624467  -9.24168222  -5.0616401   13.26311011  65.77125848\n",
      "  40.56814229 -24.31190052  40.11561186  -0.52795869 -28.85305899\n",
      "  46.14295291  47.34239086 -18.30972284  55.433756    36.15200708\n",
      "  17.38815273  12.99967452  27.26845793  34.59509352  15.76174587\n",
      "   4.24887402 -14.48121382 -27.99768749  -6.53995942  57.13269411\n",
      " -25.66160859  45.36375209  20.67487618  23.25292219 -58.95521989\n",
      "   5.35897522  -8.8413156   23.11207146  -6.34083919   1.68099323\n",
      "  35.9619321  -34.92991459   6.60528012  11.78631536 -19.50306884\n",
      "  36.60625406  28.2143665   -7.51901333   6.80540994  -9.13553184\n",
      "  -5.68859507  14.12458788 -69.59697274  38.4007097   15.72081357\n",
      "  -7.01780049   0.12888039   5.77669835  23.60206336 -18.39649248\n",
      "  32.34298727   8.77720418 -28.65743294  35.52464499  -0.68494407\n",
      " -12.42955995  21.78546213  51.23837535  15.78181243   5.80620441\n",
      "   0.33363431  36.49017056  15.63821814  32.36812309  21.67314551\n",
      "  25.76225492  33.16189222 -28.19234754 -10.03502124   6.46576509\n",
      " -14.48063497 -14.94204338   7.31931683 -36.4209731   15.74073161\n",
      "  27.18503109  48.77919888  -1.61242172   7.88555341  19.72338432\n",
      "  48.20282934  -8.39122261   5.69752269  22.84439977  12.13283577\n",
      "  -6.41479436 -24.34967191  -7.50659134  14.35352698 -25.15027322\n",
      "  73.71324435  19.05081005  52.79008469  10.1281901  -16.69327508\n",
      "  71.58222358  32.66128595  31.30263733  23.81524722   9.14307677\n",
      "  46.30074753  31.41178153  -3.89159342  56.88335696  27.25959761\n",
      "  25.27497558  23.41555939  -6.3668888   10.55248651  -5.26727165\n",
      " -38.0702586   37.20609911  13.03259527  38.03656082   2.3044116\n",
      "  11.36400264  -4.54925537  22.94771142  21.23882331 -12.64521958\n",
      " -19.8943135    1.49174085  19.25391119  -8.37369942   9.23867997\n",
      "  18.16889888 -26.91090893  46.34729388   3.90288519 -29.25782052\n",
      "  49.43744256 -31.30950253  14.29666089  23.70197355  70.62871892\n",
      "  21.76213339   1.75648764   9.91640205  27.97016353   4.6890785\n",
      "  -0.14981513 -21.85038917  24.38315413 -18.71506351  -4.46934038\n",
      " -33.17339937  20.76555646  55.1733889    3.00954426 -31.71558807\n",
      "   2.4484483   -9.32185836   8.2948603   25.49779946  44.81907185\n",
      "  13.4284342    2.15374272  56.55749156  22.85059343  33.33105548\n",
      " -24.64302545  25.33556271  24.13245808   6.69260823 -16.19885577\n",
      "  27.37411648 -24.27090997  10.96786058  35.47000442  -2.948911   -11.5180975\n",
      "   4.91654066   3.68046112  42.10557342  27.78964477   8.45696436\n",
      " -14.39318484  18.02983577 -15.86479507  24.01070292 -25.53596563\n",
      "  18.67198262   7.65551021 -18.03659252  42.20046837  15.54364541\n",
      " -26.77760197  38.36373974  39.61272661  -8.13879931   0.57972038\n",
      "  54.90265687 -16.77237669  -2.77779386  17.8118404  -15.24256055\n",
      "   8.05688528  -3.89087054   5.52587706   1.16660102  44.58865581\n",
      " -41.49889965  -2.79013908  43.44673021  20.85881067  36.17683345\n",
      "  20.07861899 -37.0317262   26.55155518  11.93164109   0.8337348\n",
      "  -4.56403639  63.75862247  23.24598797  71.49995552  49.59110041\n",
      "   2.30551538 -13.77465895 -22.74667225   7.15134967  33.87936416\n",
      "  53.06279527   0.92318895  26.95391275  41.16876807 -23.65335537\n",
      "  40.55691129  27.37441432  56.6580804  -19.93090056  19.03233732\n",
      " -21.14294929  34.15683539   0.37741676  28.89168082   7.67208945\n",
      "   7.09159698  40.62598576  32.74998753 -19.4523942   49.09463384\n",
      "  20.16731919  32.25413113  47.54457512   6.16853373 -38.26047183\n",
      "  39.08228237   3.05037556  -9.71646856 -11.44351023  13.24566104\n",
      "  17.84299984  23.17203651 -13.38898116  -7.59201128  29.87033784\n",
      "  48.06205287  13.82607517  -4.70094259  -0.81567048  12.76884398\n",
      " -49.50680804 -15.08829093  -5.56773474  20.89253561 -18.70720305\n",
      " -14.63775388 -18.15435668   6.87205257 -34.56256577 -17.68271243\n",
      "  36.92148955 -36.49082575  10.83660027  24.30875451   8.23026778\n",
      "  54.59042418   0.81921971  42.67723815 -36.61698334  31.53055839\n",
      " -17.15093903 -31.82852437  40.82753979   6.30463974  12.32052173\n",
      "  41.29892495   9.14017753  37.23488174  43.35722109  24.67482856\n",
      "  -1.13720478 -10.02527559  22.35857621  85.02721038   4.75894     34.58031116\n",
      "   5.81609049  -1.58079068   9.18215744   0.97005819  50.42996207\n",
      " -18.56433392  74.28255995   1.68531061  23.34892534   0.37042842\n",
      "  -8.75179175  27.42047877 -20.84372471  56.64718454  24.94438363\n",
      " -25.76500044  15.19902354 -22.17609175  32.83210719 -21.93481358\n",
      "  74.56738292 -10.67887706  -1.37874201 -34.15209226   8.29237952\n",
      "   2.89779435 -21.93991402   3.19654807  -3.36335125   3.17552747\n",
      "  59.68221642  -2.06814041 -15.1169101   23.74293973  -2.91719022\n",
      "  10.93166275  22.20166862  53.54457847 -17.85796631   9.69094919\n",
      "  -7.04940958  13.83895014  27.04591335  -0.18702796   0.36979594\n",
      "  16.27414987  27.38412978 -16.10950015  46.07587134   2.2028979\n",
      "   9.99079289  30.92363635   9.3881644   11.75874524   4.26078939\n",
      "   0.47590793  34.89300957  40.72060703 -19.81573622   9.17979981\n",
      "  39.59984962 -10.01241885  42.73754786  49.04143343  24.12878429\n",
      "  31.81060325  20.33359758  40.16813068   1.16715327 -18.8871113\n",
      " -24.91346573  12.07709129  49.66478759  30.21531215  25.83733585\n",
      "  46.45552717  26.01130199  24.81444108  -2.16211292  -9.86246455\n",
      " -31.98760674  22.01541713 -11.28374298 -18.57022352  14.3729362\n",
      " -18.48122623 -38.83595588  45.23733322  -6.56489918  31.77463657\n",
      " -29.33101247  -1.05665239  27.35636703  22.86329264  40.09045354\n",
      "  43.4001662  -15.90025389  -7.24098627  66.90823354 -10.97801194\n",
      "  12.97934048 -44.56373566  86.94402865  17.06663582   9.38730819\n",
      " -14.57624645  65.70029993 -44.29577233 -46.46089604  34.77904157\n",
      "  52.77854933  54.0296503    9.94035092  27.62447116  28.86300664\n",
      "   8.22721735 -50.93943821  25.45974653  40.28395764   4.81264175\n",
      "  30.43643825  36.27174643  21.34104615  71.23015685  -2.46758538\n",
      "   4.54980173  15.74898415 -12.73168841  27.02847657 -12.39202494\n",
      " -19.94301082  14.0650064   23.04455432   3.290791     5.57620459\n",
      " -26.40479566  17.04735322  21.19996366   8.75408181  24.49422815\n",
      "  -2.53466665  54.22568934 -18.77625429  27.23685255  21.3368763\n",
      "  34.65486889  47.26782875 -15.65211162 -31.9764758   37.60299903\n",
      "  -5.0496887   19.09108337  15.94028322  26.15044564 -29.82831148\n",
      "  20.12211694  35.06832427 -43.18296112  54.6618322    7.40139651\n",
      "  34.70789867 -32.63016109  27.53293031 -24.24792595  37.9972001\n",
      "  19.39070134 -20.17428426  45.10974514  34.78304307  -2.3193682\n",
      "  15.33088633  24.22777421   1.35853822  19.50620478  -7.58231382\n",
      "  40.80326177   8.12302263 -32.54134301  30.52634752 -20.71546048\n",
      "  54.39251019  40.24991633  62.06722861 -20.52575799  18.6149068\n",
      "   6.88962054 -50.66572982   2.18362654  27.62226076 -18.74725318\n",
      "  29.71123922  -8.65379819 -25.73638372  -2.73842965  -5.94913947\n",
      "  59.49036377  -4.36916204  25.7786802   -6.92137327   3.16023983\n",
      "  13.21442098 -13.35724325  -8.97344697 -23.7467114   66.78470964\n",
      "   1.77895324  20.20684883  55.43738484  19.00369136   3.68604675\n",
      "  -4.99690607  46.18560904 -35.44303892   6.7134075   -2.87469041\n",
      "  39.91707675 -32.20797127  28.07626813  -3.73623539  15.48154271\n",
      "  10.12030126  24.62191633  15.76670227  -6.6649414   24.56931937\n",
      " -16.82567881 -37.99979531  11.47959962  36.91193488 -17.72588121\n",
      "  21.49771653  17.15720313 -47.82860762  39.13988714  25.25142101\n",
      " -18.249427    30.0234924  -33.30130096  24.81112067  16.41036041\n",
      "  -0.18956966  38.22639315  14.36100971 -15.83053906   1.37412965\n",
      "  23.75030109  71.80290382  38.13690191   6.27182692   5.78776121\n",
      " -11.02552584  -3.95978343   5.21411995  40.50967298  10.49968177\n",
      " -44.77221959  13.56449297  11.58705195 -10.72693414  -2.49559807\n",
      "  -1.60319626 -25.32277489   7.62811045   7.73989694 -13.52765415\n",
      "  28.04690442  16.92596057  21.47167269   5.26522857 -19.50942038\n",
      "  -6.9925932   14.92642739  -6.98025613  -1.62878646   3.45467211\n",
      "   7.98664155  -5.64841281   5.7406464   53.98235153  38.84173499\n",
      " -29.68189127 -20.76189366  11.43414026 -33.39485097 -14.40381225\n",
      "  29.88215489  13.99933272  -6.67906228 -16.90963251   1.15933667\n",
      "  12.22867197  43.57262169   4.57353095  32.31945283  31.4442207\n",
      "  27.00462239  -5.99935085 -19.08992609  33.70292964 -32.56945579\n",
      "  -1.5305877    3.7518755   50.9207379  -31.92101167   8.2097696\n",
      "  33.16476446  20.47602828  44.80851634   2.71429448  32.03473323\n",
      " -10.03372499  38.006894    23.33671846  20.14175712  14.9210492\n",
      "  -3.94929621  13.79969538 -12.53681349  13.67203414  30.00753004\n",
      "  -7.52935281  12.02284136 -32.5647786   14.90987379  35.55467135\n",
      " -20.67291982  18.77962191 -32.32794746  41.01793546 -10.2485695\n",
      "   2.06243365  -8.2276841   31.50769255  -5.2484699   24.38990588\n",
      "  21.09595835   6.42204274  -0.7496808   14.49376505 -35.67888901\n",
      "   2.71501549 -38.19273742  57.74518065  67.06166211  10.39874541\n",
      " -11.0506926   -2.0717666   42.27170091  70.67058127  52.83308502\n",
      "  -3.3235932   33.26205047  55.66835756  49.4653813   16.06478681\n",
      "  31.67607436 -29.31231463  -4.82546317  12.52662236  -3.02795462\n",
      " -15.92850075   9.60227064 -17.68262894  24.08382409 -10.4102639\n",
      "  15.60719105 -24.45403536  44.02924532 -25.65562636 -14.72206518\n",
      "  28.12433212   5.84936506  37.58631732 -47.47593519  55.39185448\n",
      "  -6.32146074  25.33458308  39.62032228   5.72725743  29.43090168\n",
      "  37.33707314 -30.736939    23.44520362  37.27634016  -2.09124916\n",
      "   3.03688954  38.93223165  21.83714724 -19.86298139  23.35266146\n",
      " -40.30460466 -12.55168997  -0.22934021  -3.14394312   5.50647683\n",
      "  48.82925779  39.35761379  -4.60579421  14.2466912   25.12290528\n",
      " -22.16433802  25.36856316  39.55300063  12.46310664   9.83830461\n",
      "  -7.18796932  16.38779492  13.48090354  22.76191437  -5.10394446\n",
      " -23.77869783 -11.21539237   1.45274195  71.51004007 -12.26967663\n",
      "  32.6447334   12.47074972  -3.48301322  21.81443165  -6.3164452\n",
      "   7.89587723 -16.18316572   1.06965441  60.53709806 -25.12221156\n",
      "   8.5771773   -9.56352982  32.04300857   8.83331006 -27.1487614\n",
      " -10.9229682   -9.79485072  40.80314078   4.23135226 -24.04251664\n",
      "  12.69462498 -17.77964032  45.53475734 -19.01593535   7.23558349\n",
      "  -1.21825416  16.30705568 -18.04352124   8.80077858  48.6175941\n",
      "   7.9454983    7.04425339   7.04593906 -21.16685728   1.0623553\n",
      "   3.67943049  27.47792635 -37.09215794  33.88563241  -8.00780355\n",
      "  70.39012767  18.51145932 -26.8494684   24.19940354  -3.96867578\n",
      "   5.16496617  12.67112704  49.52407397 -24.75269709  15.99167155\n",
      "  24.20030785  10.26908576  17.49504375 -27.28108438   9.88497575\n",
      " -60.91958367  16.04006397  59.16675055 -17.25402829  19.72262212\n",
      " -57.84580467  23.92226921   8.51475311  33.35689528  31.6898653\n",
      "  29.69949494  64.3218039   16.72349197  -0.79430419  31.35662061\n",
      "  -1.34913879   8.64410556  16.53756821  12.30654051  -8.24997948\n",
      "  23.69573247 -52.95938859  -5.88625894  33.34910678  10.61410909\n",
      "  39.31219839   6.46416651 -39.50366588  11.56138082  15.21183372\n",
      " -14.93804269   6.98703326  16.40698018  48.50953972  26.00336834\n",
      " -45.03871939  23.56899755  34.38990068   4.95317094  -5.13187948\n",
      "  -8.5186695   45.22455466 -26.25647371  37.0819441   20.12097853\n",
      "  26.86606072  22.26562433  22.44247106  -6.05465875  32.40818175\n",
      " -14.02998593  45.61602607  33.2884846   12.46903036 -17.5724376\n",
      "  43.95381832   4.12361458   2.71463657 -19.9370746   -8.12124806\n",
      "  21.5471905   11.63210418  -5.90677122 -43.25093287   8.05740124\n",
      "   4.80046046  -2.9197278   15.22133143  42.17953641  26.34733426\n",
      "  17.92137928   9.28481321  42.19612954  21.12785141  14.65312277\n",
      "  28.38214128 -29.12299879  45.54807408  10.97865503  -0.54611802\n",
      " -13.70454087 -18.61289702  76.2668942   43.41507313   5.63866771\n",
      "  25.42900459  23.8456345   16.8024112  -25.5459796    1.25178856\n",
      " -10.78027522  14.1611678   50.74408317 -17.83508422 -40.78196127\n",
      "   8.20480783  40.7118649    4.56162841 -15.12914582 -38.57767787\n",
      "  17.41452887  48.44168646   8.38391316 -12.18545117   8.77851464\n",
      " -17.86221574  -5.37721144   8.93017514   9.25830157  62.35979335\n",
      "  24.60275766   9.18676309  28.40336932  -5.65545148  29.4421116\n",
      " -55.58431485  33.46672034  -2.80194176  32.8451041   20.58866127\n",
      "  47.24896471  24.87962811 -11.76830932  26.8450637   24.11685307\n",
      "   3.98518453   6.32203158  27.87778352 -13.82566663  32.5970415\n",
      "   6.31941822 -23.16660365   3.2698727   11.54041146  -2.78428439\n",
      "  33.69919205  37.14482371  23.25185453 -13.80599003  -6.5530019\n",
      "  -0.89669361  16.12358228  18.20251285  -2.50244962  28.13571753\n",
      "   6.15292674  -8.97933134  26.21401784  53.37191795   3.00291547\n",
      " -14.1409592   37.54288066  34.16651803 -37.96521301 -21.86682626\n",
      " -25.91320312  31.39266782  39.12316232 -18.65125796  17.9744885\n",
      " -32.50829887 -24.30773959  35.8312336  -20.46338874 -27.48903433\n",
      "  31.22172586  -6.9134233   -3.49059309 -26.04714673 -27.45300052\n",
      "  52.32496266   8.21879018 -38.16072864   5.03651435   9.18664846\n",
      "   7.35545601  12.35026922  -9.87446068  83.4518742   32.76901573\n",
      "  12.09176192   5.36694948  10.03618419]\n"
     ]
    }
   ],
   "source": [
    "x = np.random.normal(10, 25, (1000))\n",
    "print x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\python27\\lib\\site-packages\\ipykernel_launcher.py:10: RuntimeWarning: invalid value encountered in log\n",
      "  # Remove the CWD from sys.path while we load stuff.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x8c54990>]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+H/Vl2WcxUye2ojmk82vgGgAzmwmkAG1RbE9EJG7MqchhU1Mn7kzz7BNkHv7P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\n6/6wuQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8edcd10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0, 8, 0.0001).reshape((80000, 1))\n",
    "y0 = np.cos(x)\n",
    "y1 = 1 - x**2/2\n",
    "y2 = y1 + x**4/24\n",
    "y3 = y2 - x**6/720\n",
    "y4 = y3 + x**8/40320\n",
    "y5 = y4 - x**10/3628800\n",
    "y6 = y5 + x**12/479001600\n",
    "y7 = y6 - x**14/87178291200\n",
    "z = np.log(y7 + )\n",
    "plt.plot(x, y7)\n",
    "plt.plot(x, z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "age                  int64\n",
       "workclass           object\n",
       "education_level     object\n",
       "education-num      float64\n",
       "marital-status      object\n",
       "occupation          object\n",
       "relationship        object\n",
       "race                object\n",
       "sex                 object\n",
       "capital-gain       float64\n",
       "capital-loss       float64\n",
       "hours-per-week     float64\n",
       "native-country      object\n",
       "income              object\n",
       "dtype: object"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "data = pd.read_csv('census.csv')\n",
    "income_raw = data['income']\n",
    "data.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>capital-gain</th>\n",
       "      <th>education-num</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>39</td>\n",
       "      <td>2174.0</td>\n",
       "      <td>13.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>50</td>\n",
       "      <td>0.0</td>\n",
       "      <td>13.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>38</td>\n",
       "      <td>0.0</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>53</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>28</td>\n",
       "      <td>0.0</td>\n",
       "      <td>13.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age  capital-gain  education-num\n",
       "0   39        2174.0           13.0\n",
       "1   50           0.0           13.0\n",
       "2   38           0.0            9.0\n",
       "3   53           0.0            7.0\n",
       "4   28           0.0           13.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "data.head()\n",
    "x = data[['age', 'capital-gain', 'education-num']]\n",
    "x = x.head()\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = [1, 0, 0, 1, 0]\n",
    "las = Lasso()\n",
    "las.fit(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.01447391,  0.0003653 , -0.        ])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "las.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 ..., 0 0 1]\n"
     ]
    }
   ],
   "source": [
    "x = income_raw.values\n",
    "print x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\python27\\lib\\site-packages\\ipykernel_launcher.py:2: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  \n",
      "c:\\python27\\lib\\site-packages\\ipykernel_launcher.py:3: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    }
   ],
   "source": [
    "income = income_raw\n",
    "income[income == '>50K'] = 1\n",
    "income[income == '<=50K'] = 0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "income = (income_raw == '>50K').astype(int)\n",
    "income.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('O')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "income.dtype"
   ]
  }
 ],
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